1. Field of the Invention
The present invention relates generally to an error correcting apparatus and more particularly to an error correcting apparatus suitable for signal transmission.
2. Description of the Prior Art
A digital signal transmission system is generally provided with an error correcting mode which carries out a standard error correction. Recently, there are known various record mediums, from which there are derived signals of various qualities. Considering that the signal transmission system may be used under severe conditions, it is proposed that the signal transmission system should also be provided with another error correcting mode which carries out an error correction which is more powerful than that of the first error correcting mode.
Error correcting codes (ECC) of the first error correcting mode are represented by, for example, (n, i, d) single error correction (SEC)-double error detection (DED) extended BCH codes, whereas error correcting codes (ECC) of the second error correcting mode are represented by, for example, (n', i', d') double error detection (DED)-triple error detection (TED) extended BCH codes where n and n' are the code lengths, i and i' the data lengths and d and d' the minimum distances, respectively. If the error correcting codes are defined by, for example, Galois field (2.sup.4), then they become (15, 10, 4) extended BCH codes for the first error correcting mode and they also become (15, 6, 6) extended BCH codes for the second error correcting mode.
The extended BCH code is reduced by one data bit from the normal BCH code, in the first error correcting mode (15, 11, 3) and in the second error correcting mode (15, 7, 5), so that the error correction ability is reinforced to provide the extensibility.
A generator polynomial G.sub.1 (x) of the first error correcting mode in case of Galois field (2.sup.4) is expressed by the following equation EQU G.sub.1 (x)=(x.sup.4 +x+1)(x+1) (1)
Further, a generator polynomial G.sub.2 (x) of the second error correcting mode in case of Galois field (2.sup.4) is expressed by the following equation EQU G.sub.2 (x)=(x.sup.4 +x+1)(x+1)(x.sup.4 +x.sup.3 +x.sup.2 +x+1)(2) PA1 Let it be assumed that M.sub.1 (x) and M.sub.2 (x) are transmission polynomials of the first and second error correcting modes. Also, assuming that S.sub.1 is the remainder when M.sub.1 (x) and M.sub.2 (x) are divided by (x4+x+1), p is the remainder when G.sub.1 (x) and M.sub.2 (x) are divided by (x+1) and S.sub.3 is the remainder when M.sub.2 (x) is divided by (x.sup.4 +x.sup.3 +x.sup.2 +1), then syndromes S.sub.1 and P are generated for the first error correcting mode, whereas syndromes S.sub.1, P and S.sub.3 are generated for the second error correcting mode. That is, the syndrome S.sub.3 is not generated in the first error correcting mode.
As described above, the syndromes S.sub.1 and P are generated in the first error correcting mode and the syndromes S.sub.1, P and S.sub.3 are generated in the second error correcting mode. Consequently, the syndrome S.sub.3 is not generated in the first error correcting mode so that the first and second error correcting modes can not be made common from both a software standpoint and a hardware standpoint. As a result, the prior-art error correcting apparatus can not be simplified in circuit arrangement.